The other arm carries a pin P. M is a mirror (2 in. by 1 in.) fastened by sealing-wax to a stout pin which is driven in, through the ends of the two arms, at the centre of the semicircle. The mirror must be adjusted so that it is vertical and faces the o° mark.

Place the arm P so that the end of the slit in it lies exactly over one of the degree marks. Move the arm T until the image of the pin in the mirror can be seen through the tube just behind the thread. Read off the angles.

19. Measurement of Small Deflections. We may here refer to a very useful application of the law of reflection in measuring small angles, e.g. in observing and measuring small deflections of a suspended magnet. The method consists in attaching a small mirror to the magnet, and allowing a beam of light to fall normally upon this. If now the magnet moves through any angle, the mirror moves with it, and the reflected beam moves through double the angle.

If

S

This we have already proved in Expt. 12. It also follows from the law of reflection. For let st (Fig. 19) be the position of the magnet at rest and oa a ray of light falling normally upon the mirror attached to it at a; in this position the ray of light is reflected back along its own path. now the magnet moves through an angle V into the position s't', the normal to the mirror moves through the same angle into the position ap. The angle of incidence is oap=V, and hence the angle of reflection must=V; thus the reflected ray travels along ax, making an angle 2V with its original direction (ao).

The reflected ray thus forms a long weightless pointer which rotates twice as fast as the mirror. Its position is observed by allowing it to fall upon a graduated scale mn and watching the motion of the spot of light. By placing the scale at a sufficient distance from the mirror, the motion of the latter may be magnified as much as we please.

10

Fig. 19.

20. Images in Plane Mirrors.—Let A (Fig. 20) be a luminous point and MM a plane mirror. Rays of light proceed from A in all directions; some of these fall upon the mirror and are reflected by it. Let AB be any one of these rays. At B draw the normal BC; also draw BD, making the

angle DBC equal to the angle ABC. Then by the law of reflection (Art. 17) BD is the reflected ray. To an observer

C!

whose eye is placed any

where along BD the light

M

B

AV

Fig. 20.-IMAGE OF POINT IN PLANE
MIRROR.

Now, since AA' and CB are parallel (both being perpendicular to the mirror), the angles CBA and BAM are equal; and so also are the angles CBD and BA'M. But the angles CBA and CBD are, by the law of reflection, equal; therefore the angle BAM is equal to the angle BA'M. Thus in the triangles AMB and A'MB the base is common, the angles at A and A' are equal, and the angles at M are right angles. Hence the two triangles are equal, and the side A'M is equal to AM.

Hence

A' is as far behind the mirror as A is in front of it. A' is a fixed point. We have supposed AB to be any one of the rays falling on the mirror (and lying in the plane of the paper). Hence any other ray such as AB' will also after reflection appear to come from the same point A'; it will be reflected along B'D', and the line D'B' produced backwards will pass through A'.

All rays diverging from A appear, after reflection in the mirror, to diverge from A'. A' is called the image of A. An observer looking at the mirror sees the image by means of a small pencil of these divergent rays. The position of the image does not depend upon the position of the observer's eye. It is not necessary that the mirror should extend right up to (or opposite) the object A; thus in the figure the portion BB' of the mirror alone is required in order that the observer may see the image A'.

The reflected rays do not really proceed from A' but only appear to do so; A' is therefore called an apparent or virtual image.

We have thus shown that a pencil of divergent rays falling on a plane mirror remains divergent after reflection. It will be a useful exercise for you to draw a diagram showing that a pencil of convergent rays remains convergent after reflection, also that a beam of parallel rays remains parallel after reflection.

21. Summary and Definitions. -The image of a point in a mirror is a corresponding point from which rays of light diverge (or appear to diverge) after reflection from the mirror.

If the rays of light after reflection from the mirror really diverge from the point, it is called a real image; but if they only appear to diverge from the point, it is called a virtual image.

The position of the image of a point in a plane mirror is found by drawing a perpendicular from the point to the mirror and producing it until its length is doubled.

22. We can now easily find by geometrical construction the position and size of the image of an extended object produced in a plane mirror.

Let AB (Fig. 21) be the object and MM' the mirror. From A draw a perpendicular to the mirror and produce it until its length is doubled. The point A' thus found is the image of A. In the same way the image of B is formed at B', which is as far behind the mirror as B is in front of it. Similarly the images of points intermediate between A and B are formed at corresponding points between A' and B'. Thus a complete image A'B' of AB is obtained.

From every point on the object rays of light proceed towards the mirror and, after reflection, appear to come from the corresponding point of the image. In Fig. 21 are shown the paths of the pencils of light by which an observer sees the extreme points of the image. When the observer's eye is in the position shown, the only part of the mirror required for the formation of the image is that lying between C and D.

The image is virtual and erect it appears to be as far behind the mirror as the object is in front of it, and is of the same size and shape as the object.

But the appearance of the image is not exactly the same as that of the object facing the mirror. It is affected by what is known as lateral inversion. You will best understand what this is by placing a printed page in front of a looking-glass and trying to read the print in the image. The letters are all erect,

A letter p appears in

but the words read from right to left. the image as a letter q (Fig. 22). A page of type, as set up by a printer, can be read by holding it in front of a mirror.

The effects of this lateral inversion can frequently be observed by looking at the face of a friend in a mirror. Our faces are never perfectly symmetrical, and so we do not quite see ourselves as others see us.

23. Multiple Images in Inclined Mirrors-EXPT. 14.-Take two mirrors (about 4 inches square) and join two of their edges by pasting on a strip of cloth or ribbon, thus making a hinge about which the mirrors can be moved. Stand them vertically on a table with a lighted candle-end between. A number of images of the candle-flame are seen.

Either of the mirrors used by itself would give only one image. The effect observed must be due to a joint action of the mirrors, by which the light is repeatedly reflected from one mirror to the other and finally to your eye. These multiple reflections give rise to multiple images.

seven.

The number of images seen depends upon the angle between the mirrors. Adjust them so that this angle is 45°: the number of images is Gradually increase the angle to 60°: the middle image disappears and the ones on each side of it (i.e. the two nearest the hinge) coincide and form a single image. The number is now five. Increase the angle to 90° the same process is repeated and the number of images is reduced to three. Observe that the coincidence takes place when the angle between

the mirrors is contained an exact number of times in four right angles (360°); and that if this number be n the number of images is (n - 1).

It will be a useful exercise for the student to trace the paths of the rays by which these images are seen. In doing so the following principles should be borne in mind. When rays of light from a luminous object are reflected by a plane mirror, they diverge from a corresponding point at an equal distance behind the mirror: and this may be called the primary image of the object, the rays forming it having been reflected once only. If these rays fall upon a second mirror they will, after a second reflection, appear to diverge from a point as far behind the second mirror as the primary image, is in front of it. In other words, a secondary image of the object is formed by successive reflections of rays at the two mirrors. In finding the position of this secondary image, the primary image may be treated as a virtual object sending out rays of light.

This process may be repeated any number of times as long as any one of the images lies in front of one of the mirrors (i.e. in front of the plane in which the mirror lies). Thus a secondary image may after a third reflection give rise to a tertiary image, and so on.

Fig. 23 shows the appearance presented when a candle is held between two mirrors inclined at right angles. Two of the images seen are simply

primary images produced by single reflections from the horizontal and vertical mirrors respectively. The third is a secondary image, and the paths of the rays by which it is seen are shown in Fig. 24. Rays proceeding from the